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Calcium dynamics and wave propagation in coupled cells.

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Author

Date

Permanent Link

Thesis Discipline

Mathematics

Degree Grantor

University of Canterbury

Degree Level

Masters

Degree Name

Master of Science

Intercellular waves of calcium (Ca2+) are an important signalling mechanism in a wide
variety of cells within the body, crucial for cellular coordination and control. In particular
the Ca2+ concentration within smooth muscle cells (SMCs) lining the blood vessel walls
controls the cell dilation and contraction and thus the vessel radius. The process of functional
hyperaemia by which neuronal activity results in a localised response of increased
blood
ow via the dilation of SMCs is associated with multiple pathologies such as cortical
spreading depression (CSD). This process can be modelled by a `neurovascular unit
(NVU)' containing a neuron, astrocyte, and the SMC and endothelial cell (EC) within
the vessel wall.
Our research consists of modelling the Ca2+ dynamics of a both a single SMC and
two coupled SMCs (via an intercellular Ca2+
ux) mainly with the minimal nonspatial
Goldbeter et al. (1990) cell model. This is compared with the more complex model of a
SMC/EC `unit' which also includes the in
uence of neuronal stimulation on the SMC. The
Ca2+ dynamics of both models are found to be similar in structure: the system will be
either excitable, nonexcitable or oscillatory depending on a model dependent parameter
controlling the rate of inotisol trisphosphate (IP3) induced Ca2+ release into the cell.
However the SMC/EC model also produces small amplitude oscillations and bistability
when neuronal stimulation is high and the model parameter is low. The behaviour of a
coupled cell system is seemingly model independent: in particular an excitable coupled
with an oscillatory or two nonidentical coupled oscillatory cells will exhibit qualitatively
di erent behaviour when weakly coupled such as variable amplitude oscillations.
The formation and propagation of Ca2+ waves are simulated by the Goldbeter et al.
(1990) model in a two dimensional (2D) spatial medium; spatial curvature is then introduced
by simulating the model on a torus. When the local dynamics of the medium are
spatially constant a new wave solution in the form of a stable wave segment when there
is some gradient in Gaussian curvature. When the local dynamics of the medium are
spatially varied, spiral waves or apparent spatiotemporal chaos are produced when the
rate of di usion is low and either the surface is strongly curved or the initial conditions
(ICs) of the medium are su ciently inhomogeneous. Based on the similarities in the
nonspatial results the spatial Goldbeter et al. (1990) model could provide insight into the
behaviour of the corresponding complex spatial SMC/EC model.